First of all, students are stratified according to their mathematical knowledge and thinking ability. And according to different levels of students to develop different levels of teaching objectives and teaching strategies.

Level A: Good mathematical foundation and thinking ability.

Layer B: Basic mathematics is average, and thinking ability is average or good.

Layer C: The math foundation is low, and the thinking ability is average, or the thinking ability is good but the math foundation is poor, and the learning quality is poor.

D layer: poor mathematical foundation, average or low thinking ability.

After students are stratified, different levels of teaching objectives and teaching strategies are formulated for students at different levels:

A layer: top students. Put forward higher requirements and give them a small stove. Ask them to read as many math extracurricular books about problem solving and math competitions as possible besides completing textbook exercises, and encourage them to ask math questions, learn more by themselves and solve more problems.

B layer: some of them can be converted into a layer. Improve their interest in learning mathematics, encourage them to ask more questions in class, encourage them to teach themselves, encourage them to solve more problems, and ask them to strive for excellent results in exams and catch up with the best students.

C layer: improve their enthusiasm for learning mathematics, improve their mathematical foundation and mathematical thinking ability, and turn some of them into B layer. Encourage more questions and counseling to improve their interest in learning mathematics and solving mathematical problems. They are required to get more than qualified results in the test.

D layer: strive to improve their mathematical foundation and mathematical thinking ability, and improve their enthusiasm for learning mathematics. Some of them are transformed into C-level or even B-level. Patience, counseling, education, encouragement, asking as many questions as possible, improving their interest in listening to math classes, requiring them to complete their homework and strive for passing the exam.

Second, the practice and experience of stratified teaching in classroom teaching.

From 2009 to 20 12 school year, I worked as a math teacher in classes 09 1 and 096 in our school. Class 096 used the traditional teaching method, and class 09/kloc-0 tried the layered teaching method. Here's what I did:

1. In classroom teaching, I adopt different learning guidance methods for students at different levels, so that students at all levels can understand and master mathematics knowledge and develop their own abilities.

In the classroom, students in Class A and Class B are encouraged to explore problems (examples, exercises or math problems put forward by teachers and classmates), discuss problems, and finally find out the answers independently or under the guidance of teachers, and encourage them to question the existing answers (or solutions and proofs) and make multiple solutions to math problems, so as to cultivate their innovative consciousness and creative thinking ability. For students of Grade C and D, individual counseling is also strengthened after explaining the teaching content.

Review questions before class, classroom exercises and homework are all aimed at students of different levels. General classroom exercises and homework are divided into basic questions (required) and improvement questions (optional). Encourage students at the A and B levels to do improvement problems, while students at the C and D levels may not do them, but still encourage them to do as much as possible. They can do a few questions if they can.

2. Give more examples that students are interested in or adopt multimedia teaching methods to improve students' perceptual knowledge of mathematical concepts, theorems and properties and improve their interest in learning mathematics.

The students in Class 09 1 of Grade C and D have a poor foundation. Once, I found that they always treat solving equations as formula problems, knowing that they don't understand the same solution principle of solving equations, so I guided them to know the same solution principle of solving equations: I want to know how many fingers the last classmate in your class has, and now I want to compare the hand index with the last classmate. If it's the same, I want the third from the bottom. Because the hand index of the two classmates is the same before and after class, I can know the hand index of the last classmate just by looking at the hand index of the previous classmate. Then, I will use this example to compare the principle of understanding the same solution equation:

Through this example, students' interest in learning is improved, and students at C and D levels understand the understanding principle of the same solution equation. In the future, they will follow the steps of solving the equation and understand the equation with the same solution.

3. Guide students from less to more, so that students at all levels can get the inspiration they need.

In the teaching of trapezium midline theorem in junior two, I adopted the following methods for hierarchical teaching:

Ask students to recall the triangle midline theorem and the concept of trapezoid midline first. (Encourage C and D students to answer)

After the students answered, I asked a question: Do the trapezoid median line theorem and triangle median line theorem have similar properties? Let the students draw and discuss, and then tell the answer or guess the answer.

After the students say the answer (the center line of the trapezoid is parallel to the two bottoms, which is equal to half of the sum of the two bottoms of the trapezoid), I write the answer on the blackboard as a proposition, and then let the students draw pictures on this proposition and write the known proofs.

Then draw a blackboard for B-level students and write down your known verification of this proposition. C-level and D-level students ask questions after writing on the blackboard, and the students answer, and the teacher instructs them to correct the known verification written by the students.

It is known that the center line of trapezoidal ABCD is MN.

Verification: MN∑BC, MN= 1/2(AD+BC)

Then, I ask students to write or think about the proof process (requirements: A-level students use more than two methods to prove, B-level students write the whole process of a proof method, and C-level and D-level students think and try to write part or all of the proof process of a proof method)

My derivative 1: Can it be proved by the triangle median theorem? After the guidance, check how many students at A and B levels can write the proof process (many students have not written the proof process).

I will guide you again. 2. How to transform the trapezoid you drew into a triangle with the middle line of the trapezoid as its center line?

Let the students discuss the problem before proving it. I'll check again how many students will write the proof process. (It is found that a few of the A-level students, most of the B-level students, and those of the C-level and D-level students can't write the proof process yet)

I'll guide you again. 3. As shown in the trapezoidal ABCD, after D, M is the reverse extension line of the ray intersection BC, and the △DEC of point E is obtained. After the guidance, I will check how many students will learn to write the proof process (I found that most students in grades B, C and D still haven't written the proof process).

Let me guide you again: As shown in the figure (above), can you prove that the line segment MN is the center line of △DEC? Point n is already the midpoint of the DC edge. What should be proved first to prove that MN is the center line of △DEC?

Ask students at levels B, C and D, and the students answer: Prove that point M is the midpoint of the DE edge, that is, DM=EM. Let me ask again: What should I prove first to prove DM=EM? (Asking students at levels B, C and D) Student A: Do you want to prove △ ADM △ BEM? Is it enough to prove that these two triangles are congruent? (Ask C and D students until they get it right)

Then, draw a B-level student and write down his proof of this proposition on the blackboard. After the students finished writing on the blackboard, I asked the A and B students to correct it. Ask students who can't write the C and D certification process to carefully look at the correct certification process on the blackboard, and encourage them to ask questions where they don't understand. And let the students at A and B levels answer. Finally, in order to make students at C and D levels better understand, I will explain the idea and process of proving this proposition.

Then, look at the other proof methods of this proposition by students of A and B levels, and select some of them to explain their own proof ideas. I wrote down the students' opinions on the certificate on the blackboard, and made comments and revisions.

Comparison of teaching effect: (1) As far as the teaching progress is concerned, the 09 1 class of stratified teaching is faster than the 096 class of traditional teaching method. Because in class 096, many students don't master some math classes well enough, they often have to make up lessons and increase practice classes, but in class 09 1, it is not so necessary to do so.

(2) Comparison of math scores in the year-end exam between the two classes:

Obviously, the hierarchical teaching method is better than the traditional teaching method. Poor students have decreased and excellent students have increased. Because the traditional teaching method mainly takes care of the whole, and often does not emphasize the individual, it cannot really teach students in accordance with their aptitude. Although hierarchical teaching method is also a kind of class teaching, it requires teachers to emphasize individuals (at least some students at a certain level), that is, teaching students in accordance with their aptitude at a certain level, which reflects the teaching of students in accordance with their aptitude, so it can better improve students' learning enthusiasm and mathematical thinking ability, thus improving the teaching effect of mathematics.